The 22-year-old centre-back has opted for a new challenge in Serie A, joining on an initial loan deal from the Bundesliga side
The Serie A club have paid €4 million up front, with a further €9 million due if they want to complete a full transfer for the centre-back from the 2016-17 season.
“I’m absolutely delighted to be able to wear the Roma jersey,” he told his new side’s official website.
“I’ve come here to win titles, to win the Scudetto. I would like to thank all the Roma fans and promise them that I will give everything for this club.”
Rudiger made his debut for Germany in May 2014 and has gone on to win six caps with the national team.
The 22-year-old old rose from Stuttgart’s youth team to become a first-team regular, and departs the Bundesliga side having made 66 appearances.
Roma have been on the lookout for defensive reinforcements having sold Alessio Romagnoli to Milan, and Mapou Yanga-Mbiwa to Lyon.